1. Field of the Invention
The invention relates generally to a cone beam computed tomography (CT) imaging system, and more specifically to a simplified method and apparatus for image reconstruction in such a system.
2. Description of the Prior Art
Recently a system employing cone beam geometry has been developed for three-dimensional (3D) computed tomography (CT) imaging that includes a cone beam x-ray source and a 2D area detector. An object to be imaged is scanned, preferably over a 360.degree. angular range and along its entire length, by any one of various methods wherein the position of the area detector is fixed relative to the source, and relative rotational and translational movement between the source and object provides the scanning (irradiation of the object by radiation energy). The cone beam approach for 3D CT has the potential to achieve 3D imaging in both medical and industrial applications with improved speed, as well as improved dose utilization when compared with conventional 3D CT apparatus (i.e., a stack of slices approach obtained using parallel or fan beam x-rays).
As a result of the relative movement of the cone beam source to a plurality of source positions (i.e., "views") along the scan path, the detector acquires a corresponding plurality of sequential sets of cone beam projection data (also referred to herein as cone beam data or projection data), each set of cone beam data being representative of x-ray attenuation caused by the object at a respective one of the source positions.
As well known, and fully described for example in the present inventor's U.S. Pat. No. 5,257,183 entitled METHOD AND APPARATUS FOR CONVERTING CONE BEAM X-RAY PROJECTION DATA TO PLANAR INTEGRAL AND RECONSTRUCTING A THREE-DIMENSIONAL COMPUTERIZED TOMOGRAPHY (CT) IMAGE OF AN OBJECT issued Oct. 26, 1993, incorporated herein by reference, image reconstruction processing generally begins by calculating Radon derivative data from the acquired cone beam data. The Radon derivative data is typically determined by calculating line integrals for a plurality of line segments L drawn in the acquired cone beam data. In the embodiment described in detail in the 5,257,183 patent, Radon space driven conversion of the derivative data is used to develop an exact image reconstruction of a region-of-interest (ROI) in the object.
A cone beam data masking technique which improves the efficiency of the calculation of the Radon derivative data in such a Radon space driven technique is described in the present inventor's U.S. Pat. No. 5,504,792 entitled METHOD AND SYSTEM FOR MASKING CONE BEAM PROJECTION DATA GENERATED FROM EITHER A REGION OF INTEREST HELICAL SCAN OR A HELICAL SCAN, issued Apr. 2, 1996, also incorporated herein by reference. The masking technique facilitates efficient 3D CT imaging when only the ROI in the object is to be imaged, as is normally the case. In the preferred embodiment described therein, a scanning trajectory is provided about the object, the trajectory including first and second scanning circles positioned proximate the top and bottom edges, respectively, of the ROI, and a spiral scanning path is connected therebetween. The scanning trajectory is then sampled at a plurality of source positions where cone beam energy is emitted toward the ROI. After passing through the ROI the residual energy at each of the source positions is acquired on an area detector as a given one of a plurality of sets of cone beam data. Each set of the cone beam data is then masked so as to remove a portion of the cone beam data that is outside a given sub-section of a projection of the ROI in the object and to retain cone beam projection data that is within the given sub-section. The shape of each mask for a given set of cone beam data is determined by a projection onto the detector of the scan path which is above and below the source position which acquired the given set of cone beam data. The masked (i.e., retained) cone beam data is then processed so as to develop reconstruction data An exact image of the ROI is developed by combining the reconstruction data from the various source positions which intersect a common integration plane. Hence, the masks are commonly referred to as "data-combination" masks.
Data-combination masks can also be used to improve the efficiency of the calculation of the derivative data in a detector data driven technique, such as the simplified ramp filter technique described in the present inventor's U.S. Pat. No. 5,881,123 entitled SIMPLIFIED CONE BEAM IMAGE RECONSTRUCTION USING 3D BACKPROJECTION, issued Mar. 9, 1999, also incorporated herein by reference. This simplified technique reconstructs the image using 2D approximation data sets formed by ramp filtering the masked cone beam data in the direction of the projection of a line drawn tangent to the scan path at the source position that acquired that set of cone beam data. Although this technique is less complex than the prior techniques, the reconstructed image is not exact.
Accordingly, U.S. patent application Ser. No. 09/162,303 entitled ADAPTIVE MASK BOUNDARY CORRECTION IN A CONE BEAM
IMAGING SYSTEM, filed Sep. 28, 1998, now U.S. Pat. No. 6,084,937 issued Jul. 4, 2000, and also incorporated herein by reference, describes a technique for computing 2D correction data which, when combined with the ramp filtered 2D approximation data sets, yields an exact image reconstruction. The 2D correction data basically comprises a point spread function representative of image reconstruction processing for each point on the detector which interesects the boundary of the data-combination mask. However, the techniques disclosed therein require circle scan paths near the top and bottom edges of the ROI when only an ROI is to be imaged. It would be desirable to provide such a simplified image reconstruction processing without the requirement of circle scan paths near the top and bottom edges of the ROI.
The present inventor's allowed U.S. patent application Ser. No. 09/343,770 entitled EXACT REGION OF INTEREST CONE BEAM IMAGING WITHOUT CIRCLE SCANS, filed Jun. 30, 1999, incorporated by reference herein, improved upon the invention described in the forenoted U.S. Pat. No. 5,504,792, by providing an exact image reconstruction of an ROI in an object without the requirement that the source scan path have top and bottom circle scan paths near the top and bottom edges of the ROI. Furthermore, the improvement is applicable to both of the Radon space and detector driven types of image reconstruction processing. As described in this U.S. patent application Ser. No. 09/343,770, and consistent with the techniques described in the above noted U.S. Pat. Nos. 5,881,123 and 5,504,792, when calculating the derivative data, the length of the line segments L formed in the acquired cone beam data (along which integral data is to be developed) are determined by the boundaries of the data-combination mask. Exact image reconstruction processing for source positions which are "internal" to the top and bottom edges of the ROI can use the simplified ramp filtering with 2D correction data technique of the forenoted U.S. patent application Ser. No. 09/162,303. However, when processing cone beam data acquired at source positions near the top or bottom edges of the ROI, the line segments L are divided into two groups, where in one of the groups the line segments L have one of their end points determined by a horizontal line of the mask (in a preferred embodiment this horizontal line is the x-axis of the mask), instead of having both of the endpoints determined by the outer boundaries of the mask. When processing along the line segments L in this one group, acquired cone beam data which resides along lines L on the other side of the horizontal axis of the mask are not used. Thereafter, integral data is calculated for the line segments L having their endpoints limited by the horizontal axis in the mask, and the data is further processed so as to develop contributions to a 3D image reconstruction of the ROI in the object.
More specifically, when processing cone beam data acquired at source positions near the top or bottom edges of the ROI, the Filtered Backprojection (FBP) image reconstruction technique described in the forenoted U.S. patent application Ser. No. 09/343,770 can be used. FBP image reconstruction consists of two different kinds of processing: the first kind is 2-dimensional (2D) and the second kind is 3-dimensional (3D). In the 2D step each cone beam projection image is processed in a 2D space, and in the 3D step the processed 2D images are backprojected into a 3D object space. As shown in FIGS. 1A and 1B, the 2D step consists of the following 4 FBP image reconstruction sub-steps for processing the cone beam data acquired at each of a plurality of the source positions (S.sub.i) along the scan path:
1. Compute a 1D projection (i.e., a line integral) of the cone beam image acquired on a detector plane 100, at each of a plurality of angles .theta.. This step is illustrated in FIG. 1A for a given angle .theta..sub.1 of a plurality of angles .theta..sub.1. A 1D projection 102 is shown at coordinates r, .theta..sub.1 comprising the integrated values of the cone beam image 104 on detector plane 100 along a plurality of parallel lines L(r, .theta..sub.1) that are normal to angle .theta..sub.1, each line L being at an incremental distance r from an origin O. As shown and described below in conjunction with FIGS. 3A and 3B illustrating processing of cone beam data acquired near the top edge of the ROI, the lengths of the lines L will be limited using the masking techniques of the forenoted U.S. patent application Ser. No. 091343,770. Generally, if the detector plane 100 comprises an N by N array of pixels, then the number of angles .theta. is typically given by .pi.N/2.
2. Filter (differentiate) each 1D projection 102 in accordance with a d/dr filter, resulting in a new set of values at each of the r, .theta. coordinates, such as shown by the derivative projection 106 for the angle .theta..sub.1, shown in FIG. 1A. Note, the sum (integration) of the resulting values at these r, .theta. coordinates yield a quantity proportional to the Radon derivative for an integration plane Q(r, .theta.), as described above for Radon space driven image reconstruction processing. PA1 3. As illustrated by FIG. 1B, backproject the derivative projection 106 from each angle .theta. into a 2D object space 107 (which coincides with the detector plane 100). Lines 108 are representative of this backprojection, and spread the value from each r coordinate into 2D space 107 in a direction normal to each .theta., thereby developing contributions to a backprojection image 109. Note, 2D object space 107 has a size corresponding to a virtual detector which is enlarged (compared with detector having a height corresponding to the pitch of the scan path), so as to cover the entire ROI in the object. This enlargement is required because the calculated Radon data affects the reconstruction of the entire Q plane, and not just the partial plane represented by the data combination mask. PA1 4. Perform a 1D d/dt filtering of the backprojection image formed in 2D space 107 by step 3. The 1D filtering is performed in the direction of the scan path, i.e., along lines 110, where t points in the direction of the projection of a line drawn tangent to the scan path.
As shown in FIG. 1B, the 3D step comprises performing a weighted 3D backprojection of the resulting data from 2D space 107 (i.e., from each pixel in the detector) onto a plurality of sample points P in a 3D object volume 112. The density assigned to each point P is weighted by the inverse of the square of the distance between the sample point and the location of the x-ray.
Although this technique allows exact image reconstruction without the requirement of a circle scan path near the top and bottom edges of the ROI in the object, the 4-substeps of 2D processing as described above, is relatively complex and time consuming, since it is required to be repeated for each angle .theta..
It would be desirable to provide a simplified (i.e., less complex and time consuming) image reconstruction processing, such as that described in the forenoted U.S. Pat. No. 5,881,123, which does not require the use of circle scans near the top and bottom edges of the object being imaged.